Materials vs. Texture Sets
A "texture set" is the full set of textures for a material, as you've listed above.  For example, diffuse, specular, roughness, metalness, etc. = 1 texture set.  If you download a PBR material from a site like CC0 Textures, what you get is 1 texture "set."

I'm interpreting this requirement to mean that they want separate materials with separate texture sets.  In other words, don't put the leather and wood on the same maps.  You could of course put the all of them into one texture set, with just different parts of a map defining different material parameters but it sounds like they want it separated by material.

So the "leather" material would have its own diffuse, spec, etc., and the "wood" material has its own textures as well.  Sounds like this was your plan anyway.

Secondly, you are correct that Specular and Metalness are usually two different workflows.  I think your client wants the flexibility to be able to use either one.  Maybe they aren't sure which renderer they will use in the end.